0342804 20240103193459.620100513235959.9 000278692300009 77955230142 10.1016/j.ijar.2010.01.014 14 s. cav_un_epca*02567740888-613X515 (2010)578-586Elsevier learning Bayesian networks standard imset inclusion neighborhood geometric neighborhood GES algorithm cav_un_auth*0101202 Studený Milan Matematická teorie rozhodování Department of Decision Making Theory MTR MTR UTIA-B Department of Decision Making Theory Ústav teorie informace a automatizace AV ČR, v. v. i. cav_un_auth*0101228 Vomlel Jiří Matematická teorie rozhodování Department of Decision Making Theory MTR MTR UTIA-B Department of Decision Making Theory Ústav teorie informace a automatizace AV ČR, v. v. i. cav_un_auth*0261765 Hemmecke R. DE http://library.utia.cas.cz/separaty/2010/MTR/studeny-0342804.pdf IAA100750603 GA AV ČR CZ cav_un_auth*0216427 1M0572 GA MŠk CZ cav_un_auth*0001814 2C06019 GA MŠk CZ cav_un_auth*0216518 GA201/08/0539 GA ČR cav_un_auth*0239648 CEZ:AV0Z10750506 Basic idea of an algebraic approach to learning Bayesian network (BN) structures is to represent every BN structure by a certain (uniquely determined) vector, called a standard imset. The main result of the paper is that the set of standard imsets is the set of vertices of a certain polytope. Motivated by the geometric view, we introduce the concept of the geometric neighborhood for standard imsets, and, consequently, for BN structures. Then we show that it always includes the inclusion neighborhood}, which was introduced earlier in connection with the GES algorithm. The third result is that the global optimum of an affine function over the polytope coincides with the local optimum relative to the geometric neighborhood. The geometric neighborhood in the case of three variables is described and shown to differ from the inclusion neighborhood. This leads to a simple example of the failure of the GES algorithm if data are not ``generated" from a perfectly Markovian distribution. cav_un_auth*0261766 PGM 2008 2011 BA 4 A 4a 20231122134022.4 http://hdl.handle.net/11104/0185432 COMPUTERSCIENCEARTIFICIALINTELLIGENCE 1.720 0.222 5.5 0.00415 0.521 1384 63 1.454 Q1 55.614 65.278 Q2 Q1 2010 Soubory v repozitáři: studeny-0342804.pdf 77955230142 SCOPUS 000278692300009 WOS cav_un_epca*0256774 International Journal of Approximate Reasoning 0888-613X 1873-4731 Roč. 51 č. 5 2010 578 586 Elsevier